Question

Fully explain your answers for all questions.

Q1. A password must have exactly ten symbols, each symbol being one of the 26 lower case letters or one of the five special symbols as follows: *, &, %, $, #. (You can leave your answer as a mathematical expression rather than a number ).

(a) How many such passwords are possible in total?

(b) How many passwords are such that all their symbols are distinct?

(c) How many passwords use only letters, and in alphabetical order, where letters may not be repeated?

(d) How many passwords use only letters, and in alphabetical order, where letters may be repeated

Answer 1

(a) The number of possible passwords is calculated as follows: Number of passwords = 31X31X31X31X31X31X31X31X31X31 Because for each place we have 26 letters plus 5 special symbols. (6) The number of possible passwords is calculated as follows: Number of passwords = 31x30 x 29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 Because each time one value will be reduced by one. (c) The number of possible passwords is calculated as follows: 26! Number of passwords=0 26 x 25 x 24 x 23 x 22 x 21 x 20 x19x18x17 Because 26 letters can be arranged in alphabetical order and if they don't need to be repeated the denominator term will have 10 values as shown above. (d) The number of possible passwords is calculated as follows: 26! Number of passwords == 26 x 25 x 24 x 23 x 22 x 21x 20 x19x18x17 Because 26 letters can be arranged in alphabetical order and repetition is allowed. Good luck with your studies!!!